Wave transmission system and method for synthesizing a given electrical characteristic



May 26, 1953 w. R. BENNETT 2,640,105 SYNTHESIZI WAVE TRANSMISSION SYSTEM AND METHOD FOR NG A GIVEN ELECTRICAL CHARACTERISTIC 4 Shee*t sSheet 1 Filed Oct. 10. 1947 w an INVENTOR 7 By w R. BENNETT ATTORNEY y 26, 9 w. R. BENNETT 2 640, 05

WAVE TRANSMISSION SYSTEM ANDMETHOD FOR SYNTHESIZING A GIVEN ELECTRICAL CHARACTERISTIC Filed Oct. 10-, 1947 r 4- Sheets-"Sheet 3 FIG. 3A

.71, In n l n v I SWEEP 4 y, 4 L 7L FIG. 38

TIME

Nl/EN/TOR y n. BENNETT ATTORNEY May 26, 1953 w .Rka NN r1- 2 6 1 WAVE TRANSMISSION SYSTEM v151D METHOD FOR SYNTHESIZIN G 40, A GIVEN ELECTRICAL CHARACTERISTIC Flled Oct. 10. 1947 4 Sheets-Sheet 4 SEQQ u Emu 34am uiqmiww INVENTOR J W R. BENNETT ATLOflNEY Patented May 26, 1953 WAVE TRANSMISSION SYSTEM AND METH- OD FOR SYNTHESIZING A GIVEN ELEC- TRICAL CHARACTERISTIC William R. Bennett, Summit, N. J., assignor to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Application October 10, 1947, Serial No. 779,113

8 Claims. 1

This invention relates in general to electrical wave transmission, and more particularly to the modification of electrical signals in accordance with preselected patterns of amplitude, frequency and phase.

In accordance with usual prior art practice, desired modifications in the amplitude versus frequency and/or phase characteristics of electrical signals have been obtained by the use of networks containing as elements resistances, inductances, and capacitances combined in conformance with well-known principles of steadystate theory to produce desired effects. Circuits of the foregoing type become complicated and cumbersome when it is necessary to produce certain odd and unusual response characteristics.

More recently, systems for producing similar modifications in electrical signals have been devised in accordance with time-function theory, by taking into account the transient responses of a system to an impressed input signal which add up at successive instants to produce a desired signal in the output. Systems of the foregoing type are disclosed in Patents 2,024,900, December 17, 1935, 2,124,599, July 26, 1938, and 2,128,257,

. August 30, 1938, to N. Wiener and Y. Lee, and

in application Serial No. 731,232, filed February 27, 1947 by L. C. Peterson and R. K. Potter, now Patent 2,575,393.

It is the principal object of the invention herein set forth to improve the time-function technique of modifying electrical signals.

In accordance with the present invention, the aforesaid object is realized in a system which performs a series of functional steps including the following:

(1) Sampling an impressed electrical signal at discrete intervals, and holding each sample for a predetermined interval;

(2) Multiplying each held sample by a predetermined weighting function; and

(3) Continuously collecting the successive weighted samples to produce a desired output function.

In one embodiment, the system of the present invention comprises a cathode-ray tube and associated sampling and holding circuits. The held samples of the impressed signal are utilized to intensity-modulate a cathode-ray beam which is periodically swept over a shaped target. Output current proportional to the samples thus weighted is continuously collected in the form of secondary radiation from the target.

In another embodiment several modifications of which are described herein, a plurality of such 2 cathode-ray tubes are operated in tandem, and their outputs continuously superposed.

The invention will be better understood from a study of the illustrative embodiments which are shown in the attached drawings and described in detail with reference thereto.

Fig. 1A is a schematic showing of a system for modifying electrical signals in accordance with the teachings of the present invention which comprise a single cathode-ray tube with an associated sampling and holding circuit.

Fig. 1B is an enlarged view of a typical shaped target element of Fig. 1A.

Fig. 1C shows graphically a typical form of output current from the system of Fig. 1A.

Fig. 2A is a block diagram of a complex system in accordance with the present invention comprising a plurality of sampling and holding circuits and their associated cathode-ray tubes connected for tandem operation.

Figs. 23 and 20 show modified forms of pulse distribution systems which may be substituted for the pulse distribution system shown to the left of the line X--X of Fig. 2A.

Fig. 3A shows a series of diagrams illustrating the time distribution of the pulses from the sampling pulse generator and distributor 39 of Fig. 2A, and their corresponding time relation to the pulses impressed on the sampling circuits S1, S2,

.etc, and the voltages impressed on the sweep circuits No. 1, No. 2, etc.

Fig. 3B indicates graphically a typical form of output current realized from the systems of Figs. 2A, 2B and 20.

Fig. 4A is a block diagram of a system of the invention similar to that of Fig. 2A, except that it is adapted to utilize a weighting function having both positive and negative components.

Fig. 4B shows a typical g-function having both positive and negative components such as utilized in shaping the cathode-ray targets in the system of Fig. 4A.

Fig. 4C shows a section aa through one of the cathode-ray tubes 01+ of Fig. 4A revealing a target shaped in accordance with the positive component of the gr-function of Fig. 4B; and

Fig. lD shows a section bb through one of the cathode-ray tubes C- of Fig. 4A revealing a target shaped in accordance with the negative component of the g-function of Fig. 4B.

Realization of network characteristics by means of sampling and pulse shaping enables the designer to employ techniques not available with inductive, resistive, and capacitive elements. For example, a hypothetical network'reacts to an infinitesimal impulse impressed on its input to produce a characteristic impulse response function. If it is desired to simulate the operation of a particular network, its characteristic impulse response can be constructed in the form of a target pro-file with height proportional to the ordinates of the desired impulse response curve. A ribbon electron beam swept horizontally across the target then produces a current proportional to the height at the line of contact. By making the intensity of the beam proportional to the held sample of signal amplitude, a pulse is thereby produced which is equal to the sample multiplied by a characteristic impulse response function. Repeating this process periodically and filtering the output yields a steady state admittance function which corresponds to. the impulse response function. A filter is included in the output to remove frequencies above half the sampling frequency.

Referring to Figs. 1B. and IQ of the drawings, a system will now be described in detail which is adapted to produce; a modified electrical output signal by a series of operations such as described in the foregoing paragraph.

The circuit of Fig. 1A comprises an input section from which the electrical input signal is fed through a low-pass filter into a sampling and holding circuit S at a pulse rate which is controlled by a pulsing circuit P. The held. samples of signal are utilized to control the intensity of a beam sweeping a shaped target in the cathode-ray tube C synchronously with the pulse rate, whereby secondary radiation from the target which is proportional to the charge collected thereon passes into the output through a second low-pass filter to produce a response having the desired characteristic.

The impressed electrical signal which is to be modified enters the circuit through the terminals I and 2, and is restricted by the low-pass filter 3 to the band to j, containing its essential components. Assuming that the output of the filter 3 does no contain zero frequency asan essential component of the signal, the filter 3 is connected to the secondary coils 4a and 4b of, the step-up transformer 5, which is directly connected to the twin input circuits of the sampling and holding circuit S.

The sampling circuit S comprises the twintriode tube 1, having cathodes 8a, and 31), plates 9a and 9b, and grids i la and lib. The cathodes and plates are cross-coru1ec-ted, the cathode 8a to the plate Sb and the plate to to the cathode 8b. The grids Ha and Nb are inductively coupled through twin circuits, which include the primary coils do and 4b and secondary coil 6 of the transformer 5, to the pulsing circuit P. The pulsing circuit P comprises a synchronizingsine wave generator l2 of the desired frequency connected to trigger a sampling pulse generator l3, which may take the form of a multivi-brator or other square-wave generator known in the art. Square top sampling pulses from the output of pulsing circuit P are impressed on the primary coil 6 of the transformer 5.

The twin circuits which function to conduct the sampling pulses from transformer to the grids Ho and I'll) include substantially identical parallel combinations of condensers [4a, [4b and resistances i-Ea, 45b, which serve in each case to hold a negative bias between pulses which blocks the flow of plate current in the respective circuits except when the square top blocking pulse from the pulsing circuit P is present. When the letter is applied, both of the twin-triode circuits become conducting, providing a low resistance path for either positive or negative current from the transformer 5. Depending on whether the signal is positive or negative, current then passes from one. or the other of the plates 9a or 9b to a holding circuit comprising the condenser IT and the cathode-follower tube [8, which includes a grid 19, a cathode 20, and a plate Zl energized by a positive potential source 22. The condenser H, which is connected between the grid [9 and a junction point between the resistor 23 and the negative bias 24 in the circuit of cathode 29, then charges or discharges quickly to the signal potential, and holds this value of potential. during the interval between pulses. This same value of potential appears across the resistance 26', and is impressed in series with a suitable negative bias from the source 24 onto the control grid 25 of the cathode-ray tube C, which is of the general type disclosed by F. Gray in P tent 2,257,795., Oc ober ,1

The catho e-r y tube C compris s a l sstube 24, in one end of which is disposed an electron emitting cathode 26' energized by a potential source ,2! to produce. a beam 28 which scans a shaped target. .29 disposed in its path at the other end of the tube. The target 29 is critically shaped in a plane normal to the plane of Fig, 1A, having a vertical dimension which varies linearly in accordance with a particular weighting function which is derived in a manner which will be described in detail hereinafter. Fig. 1B shows a view of a target corresponding to a typical weight.- ing function as viewed in a plane normal to the plane of Fig. 1A along the section line a.a.

The focussing electrode 30, which, is charged to a po itiv potential y he izing ource 3|, serves to form the beam 28 into a vertical ribbon of charge, which sweeps left to right across the target 29 at a repetitive frequency which is determined by the. charge on the electrostatic deflection plates 32 connected to the output of the con! ventional linear saw-tooth sweep generator 39. Operation of the sweep generator 39. is synchronized by connection to the sampling pulse generator [3, so that the sweep of the cathode-ray beam from left-to-right across the target, is initiated at the same time that the sampling pulse is removed from the twin-triode tube T, and continues until the beam reaches. the other target edge just prior to the appearance of the next succeeding sampling pulse. The beam returns quickly to its initial position after the target has been traversed. In order to eliminate distortion of the output signal the beam 28 is blanked during the return trip by means of a blanking circuit 40 which may take the form of a generator of negative pulses, such as a multivibrator, operation of which is triggered when the sweep voltage reaches a maximum positivev value. The negative pulse output of the blanking circuit 40 is utilized to negatively bias the beam control? grid 25 below cut-01f potential during the return sweep. Because the beam 28 is ribbon shaped in a vertical plane, and because the vertical dimension of the target varies linearly with the weighting function, the area of contact of the beam with the target is at each point proportional to the weighting function in accordance with which the target is shaped.

Electrons are emitted by the target 29 throughout the area of contact by the well-known phenomenon of secondary emission, the number of ele trons emitted being. proportiona o the prodnot of the beam current and the contact area. The secondary electrons are collected by a metallic ring 33 surrounding, the target 29, and having a positive potential with respect thereto maintained by the biasing source M. The amount of current flowing in the collector ring 33 is therefore proportional to the productof the signal sample and the vertical target dimension, which represents the weighting function. This current is filtered and delivered to the output terminals 31 and 38 through a circuit which includes the coupling transformer 34 in series with the resistance element, 35, and the low-pass filtering circuit 35 which has cut-off frequency at 1 which is preferably half of the sampling frequency. The output current, as shown in Fig. 10, thus resembles a series of pulsedsamples of the input signal, each of which is a replica of the weighting function.

In order to provide a better understanding of the concepts which underlie the present invention, the operation of the circuit described in the i'oregoing paragraphs will be analyzed step by step and discussed in mathematical terms.- It will be apparent that in the system of the present invention usual current design procedures in terms of electrical network components are replaced by consideration of geometrical construction and timing arrangement, whereby a desired electrical output response is obtained by superposing a series of properly shaped pulses in critical time relation.

The physical process performed by the system of Fig. 1A may be broken down into the following functional steps.

I. The step of instantaneous sampling, in which a continuously varying signal is converted into a set of regularly spaced pulses of infinitesimal duration, is performed by the pulsing circuit P operating on the input signal through the twin-trlodes of the sampling circuit S1.

II. The step of holding the instantaneous samples, whereby the duration of each pulse is extended at constant height until the next succeeding pulse appears, is performed by the condenser which controls the grid potential of the cathode-follower tube [8, and hence the intensity of the cathode-ray beam 28.

III. The step of multiplying each pulse by the weighting function is performed by the sweep of the cathode-ray beam 28 across the shaped target 29.

IV. The final steps of collecting and filtering the output signal are performed by the continuous passage of output current from the secondary collecting ring 33 through the transformer 34 and the low-pass filter 36 to the output terminals.

In accordance with 'Step I, the wave resulting from taking regularly spaced instantaneous samples of a signal is equal to the limit as 6 becomes small of the product of the signal and an on-andoff switching function which is unity throughout a time c in each sampling period and zero the remainder of the period T. Thus if the signal is S(t), the desired result is As 6 approaches zero, the amplitude of each term in the series also approaches zero, which is to be expected because the time the switch is open becomes vanishingly small. However, 6 can'be taken not quite zero but small enough so that the amplitude factor,

wher jT=1/T, the spectrum of S(t) is confined to frequencies below Mfr/2, and Fo(t) is the time function corresponding to that part of the spectrum of the samples in the range below Mfr. If S(t) consists of a single frequency component Q cos 21rfst, l,

Note that further decrease in e does not change the relative magnitudes of components in this part of the spectrum. Equation 3 represents what is to us the essential part of the spectrum of infinitesimally narrow pulses occurring at t=tn with the n pulse having area ESQ). If we divide by e we get the essential part of the spectrum of unit impulses ofheight Sm) at time tn. Operational Step I thus sets up a train of unit impulses, each of which is multiplied by a different constant depending on the signal amplitude, e. g., (11, a2 (1.

Now assume that each instantaneous sample Shin) is multiplied by a pulse g (if-tn) where tn is the time at which the n sample occurs and g(t) is an arbitrary pulse expressed as a function of time. The result is the same as we would get if we applied S(tn) multiplied by a unit impulse (a pulse of infinite height, infinitesimal duration, and unit area) at time t=tn to a network having the impulse response function g(t). It will be recalled that g(t) for a network, which will hereinafter be referred to as the characteristic gr-function of a network, is the derivative of the indicial admittance with respect to time.

Operational Steps II and III expand the train of unit impulses produced by Step I into a train of pulses each having a shape impressed by the target 29. I

Assume that the vertical dimension of the target 29 is fashioned to correspond with a function of time g(t), in which the horizontal distance X in space is substituted for the time variable t.

If a single impulse, produced by Step I, which has a form an5(ttn where 6(t) represents a unit impulse, is operated on through functional Steps II, -III and IV, the increment of output current resultant therefrom takes the form ang(t-tn).' Thus,. the functional properties of the system of the present invention are seen to be the same as those of any linear network, such that when an impulse represented by 5(t-tn) is applied to the input of the system, the out put response is represented by unfit-tn). It is clearthat if the network, or alternatively, the system under description,- gives-such behavior tor lone :pulse, s ill ido ilikewiseior all pulses.

The operation of any such network or system is icompletely speo'i'fiediby alts-steady state transfer admittance function, which is uniquely related to the response g tt when =-a unit impulse is applied at i =by the equation:

where if :is :the steady state :trequency :of :the :input. This equation fis a direct consequence of the Fourier integral theomm discussed :for example by GeorgeeA. Campbell, the practical application of the Fourier integral, .Bell System Technical Journal, Dcto'ber 1928, vol. 'I, pp. 639-1707.

.Now, if the input wave is-expressed infterms o'f specific @steadyestate sinusoidal components, such vfor example,

lthen the output current of the system resulting Efrem such a "wave impressed 'onthe"input can he expressed in steady-state terms as-follows:

--I(t)=EA,.lY(f,l)]cs [21rf,,t+0,,+phase Y(f,,)]

'But the steady-state expansion of EH) {to embrace the frequency spectrum from m= 1 to *m 'M is actually =given hy Equation 4, sin'c'e 'Ettl Falt-f/a If -Ts 8 and the cutoff :frequency of the low pass "filter in the output 'is n72, all components of 4 except the first te-rm are-suppressed by 'th'e'lilter. "The resultant output current is I (t) =frQ|'Y('fs)| cos 'lzfii'tglsphase YUJ] "(8) Separation "of signal and undesired sharmonic compon'ents' requires that the samplingiirequency must be at least twice-asgreatrasPthe highest si nal frequency component.

Twogeneral'results applicable ?'to sampling zand holding =iol1ow ffrom :the ioriegoing ranalysis. First, "the above-derived equations provide means for calculating lth'e spectrum associated with sampling a given input funo'tion irollowed :ty holding an arbitrary wave-shape fgttl proportional to the sampled value, whereby it is apparent that a system carrying out these "functions operates *on a component 0f frequency as an admittance equal to frY(f)- The second result is the inverse -ofthe-lirst,--i. e.,that :arsp'ecifled admittance iunction Y6!) may b'e realized by sampling the signal and holding wuss wave shape found by using l/fr times the inverse Fourier integral or 5:

It is apparent that Equation 9 provides means fortcalculatin'g the vertical dimension of-the target %:29, -in 'order that t'he system rof Fig. 1A may be designed :to simulate the .action of we, network having a ;.-given transfer admittance (f);

Similarity of themesults arrivedat -matl'iemat really in the foregoing paragraphsto ithose as sociated "with 'la'p'erture :shapes win scanning systems :such :as telcphotography and television leads It the general *d'esignation of "faperture 'effeet for the transmission variations with frequency; The aperture reflect o-tassootated with holding each sampled *vahre 'iconstaznt throughout the interval Zh'cs calculated 8 and oan 'be =1sho'wn to be ule-same as that dr o. rectangular aperture. u'e'sult ailso "follows immediately liy inserting a rectangular functio'nforgd) "in Equationfi.

""otherpulse shapes which may be useful-insempling'and holding systems in placeo'f therectan gular shape utilized inthesampling'and holding circuit SpfFig-ure lA-are the exponentially and linearly decaying *typ'es, resulting, for example, ifithe sampled value isimpress'e'd as a voltage on -'a condenser, and the condenser discharges through a resistanceMtween samplinginstants.

A-practical complication whioh arises-in"systems of the-type described with reference to Fig. IA is that imany admittances imply impulse response .iunctions which exist-rover a" long period (if-time, approahhing inflmty ito secure a perfect realization. 'I-his'would mean tha't the' ho'lding ofthe sample and the sweep of the healn -ac'ross 'the tar get woul'd be -prolonged beyondthe time instant at whichlittiecomesfnecessary to 'takeanew sampie andstarta newsweep. Thisdimcultymay be overcome byproviding:severalsampling and hold- 'ing circuits which "operate in turn with each one homing its :samp'le throughout the entire time required :to reproduce the "desh'ed'pulse response function. r-Ea'oh 'rheld value then modulates its own: beam, veither tin separate "cathode ra tum-rs, 'as "will :be ='described hereinafter, or in a single multibeam'tube,'ithe sweeps i being respectively displacedin'phasezso'that'onestartslatthelbeginning of each sampling period. If the "desired im-puls'e response or i'g functiou' requires a1time TrflNT for a satisfactory approximation,fN sampling an'd holding circuits are provided, and-'Nma'thoderay tubes having-N beamsnnd'N sweeps;with a timing framework to start theioperation'ot the indit idual sets-:successively and repeat the'oycle of operation after Nssamplin'g aintervals. The relation also holds that :if the applied signal contains frequencies in thehandirom zero to :B, the maximum sampling :intervalaT lflB. It follows that 1N 2BT =Z '(10) where p -"l/Ti is the frequency'equal to the reciprocal of i the time required to approximate the pulse response iunotion.

i-According to time division or sampling theory expounded, "for example, by the present inventor ina paper Yf'I ime divisionmultiplex-systems," Bell System Technical Journal, April 1941, pages 199 to '221,-\ it is desirable to have a sampling ra'te F greater than 213 totransmit the signal band without'distortion, I he duration of. the sweep across the targetmust beigreat enough to reproduce the essential parts of the impulse response or g-ifunction.

Referring toFig. 2A of the drawings, assume that the required-sweepduration is greater than (N -1) /F, 'but less than-N/F, where N'is an integer. IThe lb'loc'k idiagramof Fig. --2A shows a system which is adapted to impress pulsed sampics of the input signal in succession on N parallel-connected circuits each of which includes a sampling and holding circuit operating on the input of a cathode ray oscilloscope, having a shaped target. The identically shaped output pulses are continuously superposed in over-lapping order in a common output circuit. The sam- 'pling and holding circuits S1, S2, Sn, and the corresponding cathode ray tube circuits C1, C2 .Cn :are identical to the circuits -S ane'c which were described-in de'tail with reference to Fig.11A ofzflzre drawings.

' JAsin theroircurt of Fig. 15., input signal-1 impressed on the terminals I and 2 and fed through the low-pass filter 3, the output of which is separately coupled to each of the sampling circuits S1, S2 Sn in the manner described with reference to the circuit S in Fig. 1A. The distribution rate at which pulsed samples of the input signal are impressed on the respective circuits S1, S2 S11 is controlled by the sampling. pulse generator and distributor 45 which may take the form of a circuit disclosed in Fig. 1A of application Serial No. 646,455, filed February 8, 1946, by L. A. Meacham, now Patent 2,486,491. 45 comprises a ring of multivibrators having a plurality of output circuits on which a succession of square-top pulses are impressed which have respective time relations such as shown by a, b, c, d and in Fig. 3A. The successive adjoining pulses from the multiple output circuits of the generator 45 are translated into a series of spaced pulses by separate passage through the respective relaxation oscillators 46a, 46b 4611 which may comprise circuits of the form,, for example, of that shown in Fig. 27, page 50 of Time Bases by O. S. Puckle, John Wiley and Sons. The successive spaced pulses from the outputs of relaxation oscillators 46a, 4611 perform the dual functions of introducing pulsed samples of the input signal in spaced time relation into the respective sampling circuits S1, S2 Sn, and controlling the tandem operation of the sweep circuits SCi, S02 and SCn which control the sweeps of the beams in the respective cathode ray tubes C1, C2 Cn. The relative time relations of the sampling pulses and the beam sweeps in the respective parallel circuits are shown by a, b, c, d, and n of Fig. 3A. The sweep cycles in each of the cathode ray tube circuits are so timed that sweep No. I electron tube C1 is initialed as soon as the sampling pulse No. l is removed; sweep No. 2 on electron beam tube 02 starts when sampling pulse No. 2 is removed, etc.

The output circuits from the secondary electron collectors of each of the cathode ray tubes C1, C2 Cn are connected through their respective transformers 47a, 41b 4111 and isolating resistors 48a, 48b 48s in parallel to a common output junction 49, from which the output current passes through the low-pass filter 36 to the output terminals 3! and 38. From the diagram of Fig. 313 it is seen that the output current comprises a series of identical pulses each shaped in accordance with a desired g-function and modified in accordance with the signal amplitude, which are superposed in overlapping order.

Numerous modifications of the system described in the foregoing paragraphs, all of which are within the scope of the present invention, will readily occur to those skilled in the art. For example, instead of using a circuit generating N pulses, such as the generator 45 of Fig. 2A, the portion of the circuit to the left of the line .r-a: may be replaced as shown in Fig. 2B by a pulse generating circuit P of the type shown in Fig. 1A having a single output, which feeds into a plurality of delay circuits 5h, 5lb 5hr in parallel, each having different values of delay corresponding, respectively, to time equal to 0, T, 2T (N-1)T seconds.

Another alternative form is shown in Fig. 2C, in which the circuit of Fig. 2A to the left of the line :c-a: is replaced by a similar pulsing circuit P having a single output which feeds into a delay line 52. Pulses delayed by the desired amounts are taken 01f at different output points 53;,53}; a 53nalong theline 52.

The circuit which determines the target shape may be computed as follows:

The pulse generator should deliver as many lobes of this function as are necessary to secure a satisfactory approximation to the desired filter. I have estimated that loss variations in the main part of the band can be heldto a few tenths of a decibel by making the g-function duration T1=10/jc. It follows from Equation 10 that one should then require N to be equal to ZOB/fc. Thus if the cut-ofi' frequency desired were half the width of the input spectrum, one would need 40 sets of sampling and holding circuits with associated pulse modulating equipment.

It will be noted that the g-function derived in the foregoing paragraphs contains both positive and negative values of amplitude, in which case the systems described hereinbefore would not function adequately to produce the desired result. A system modified to utilize 9- functions having both positive and negative components is shown in Fig. 4A of the drawing. This system is exactly similar to that of Fig. 2A except for the fact that the output currents of each of the samplin and holding circuits S1, S2 Sn are divided into two equal components which pass into separate cathode ray tube circuits, 01+, 01-; 02+, 02 etc. These cathode ray tube circuits are identical in form to the cathode ray tube circuits described hereinbefore, except for the fact that circuits 01+, C2+ Cn+ have targets shaped in accordance with only the positive components of the selected fig-function, while the cathode ray tubes 01'', Oz Cir have targets shaped in accordance with only the negatwo components of the selected g-function.

N For example, assume a selected -function has a form shown in Fig. 4B. Then the targets in cathode ray circuits (31+, 02+ Cn+ will assume the form shown in Fig. 4C, while the targets in cathode ray tubes Cr, C2" Cir will assume the shape shown in Fig. 4D. Targets of the form of Fig. 40 are disposed in tubes 01+, (22+ Cn in positions corresponding to the target 29 of Fig. 1, as indicated by the section lines aa,; and targets of the form of Fig.

4D are disposed in corresponding positions in Output currents from the cathode ray tubes 01+, 02+ Cn are respectively passed through the coupling transformers 41a, lls 4711 and the isolating resistors 48a, 48b 4811 to the common junction point 55. Similarly, output currents from the cathode ray tubes 01 02 Cn are respectively passed through corresponding couplmg transformers 41a, 41b iln and isolating resistors 43a, 48b 48s to the common junction 56. The junctions 55 and 5e are connected to opposite ends of the primary 0011 of transformer 51, whereby the components of output current separately modified by the positive and negative parts of the i -function assume e. ombinedn. pushsnull. r ati nsbcfcrl na cns. t ro h he; ow-sass.- fiitcr -35 o. th u p t rm nal 1. audit, lt c. nnareute c. hos ll d. n he a ha wi hin he. cene o h pr se t. nv t on merous ystems: quival n the n o ca e. cvis .d.. r ombinin p s y nd; nesct v x modified comp nc c utp urrent Moreover, thou h. the; pr s n nvention.- has. been: c b dby y; iii ustrct o w th:. f r: ence to typical embodiments compr s ng; certa n elements. in combination and having certain circuit arrangements, itcwill be apparenttm those skilled in-the art that the teachings of the present invention may be applied in a variety of forms toembodiments comprising other elements: in different circuit arrangements than herein disclosedl What is claimed is:

1. The method of modifying tin-electrical current which varies'in amplitude as a function-of time which comprises sampling said-currentat regular intervals, holding each of the samples so derived for a predetermined period; utilizing said heldi samples to intensitymodulate a beam of electrons, utilizing. said beam'to-sca-n atarget'at' a repetitive rate which is anintegral multiple of: said sampling rate, varying the amount of charge depositedfrom pointto point onsaid target by said. beam-in accordance Withtheproduct of. the amplitude of eachsaidheld' sample and a predetermined weighting function, and continuously collecting anoutput current which corresponds to the charge deposited onsaid target.

2'. A system. forsynthesizing agiven electricalcharacteristic which comprises combination a pulsing circuit: for. derivingsuccessive samples of an input signalv at a regularpulse rate, a storage circuit for holdingeach ofi Saidsamples for; allredetermined period; a. sourceof a bearn of electrons, means; responsive to current derived from. said storagecircuit for controlling the. intensity of saidbeam in-- accordance with the magnitudebf. said:.heldsamples; a target disposed in. the; path. oil. said beam, deflecting means responsive-to said pulsingmeans to--control said electron. beam toperiodicallyrscan said target at a scanning; rate which issynchronizedwith. said. pulse rate saidv target shaped in the direction. of scanof. saidbeam. in accordancewith a. predetermined shaping function, and means in energy transfer. relation with. said target for derivin an. Qutput current whichlis correlated with the. charge laid down. on: said target by said beam.

3. A system for synthesizing apredetermined electrical characteristic which .cQ lDrises in. comi of said beam, deflecting. mcanscontrclledby said.

pulsing circuit to actuate said. electron. beam to. periodically scan said target. ata. scanningrate. which is synchronized with said pulse rate said target having-ashape which varies. in the (ii-- rection of scanof-said beamin accordance-with.

atpredetermined weighting function andv an..o.ut- Y put.circuitresponsiveto-secondary radiation from.

12 said target for drawing an5 output; current, which: is correlated with the charge deposited-pen said; target by said beam.

4. A system; for synthesizing a; given electrical. output current which comprises incombination. a. pulsing circuit for deriving successive samples; o an. np si al t a re ula p ls ater. a:- plurality of storage circuits,. a; pulse distribm i n. ir u c n c d: to. impress. puls d: samplmz f. ai nput si n l: on ch f; said. stora e. circuits. in sta ecredv time. relation... each. said: storage circuit. operative; in staggeredtime. re.- lationforholding.aresnectivacne of saidisamnlee for; aninterval. of. thesame. predetermined-1mm.

a. plurality of sources of. beams, of: electrons;

means responsive to. current. derived; from of. said; storage; circuits. for; controlling. the; in-. tensityof arespective one of; saidbeamsainacs cordancewith the magnitudeof the sampleheld by said. individual storage circuit, a. plurality of! shaped. targets. each disposed inthe: pathof? a. respective. one of. said. beams, separate deflecteing. means. to control thescanning. motion" of each of. said beams. over its. respective target, synchronizing. means under control of saidpulse distribution meansv for controlling each: ofsaiddeflecting means to correlate scanning-motions of said respective beams with the-distribution of puls'esto said respective storage circuits, and acommon output circuit continuouslyresponsiveto: receive output current from each ofsaid' tar-- gets, whereby the individual currents are addedin staggered tirnerelation to produce-a mod-i-- fled output current.

5. A system for synthesizing a predeterminedelectrical output current which comprises in combinationapulsing circuit for deriving; successive samples of an input signal at a regularpulserate, a pulse distribution circuit; a pluralityof holding circuits,- saidpulse distribution circuit connected to impress pulsed-samples on each of said holding circuits instaggered time relation, eachof said holding circuits including a condenser responsive to assume the potential of one ofsaid pulsed samples for a" given timeinterval; a cathode -ray-tube having; a sourceof' abeam of electrons associated' with eachsaidholdingcircuit and including means for varying the intensity of saidbeam in accordance I with the currentoutput Ofsa-id' respective. holding circuit; each of said cathode-ray tubes including a target having substantially the sameshape interposed-in the path of'said beam, deflectingmeans; and an output circuit, associated with each said target and" responsive to, re-

- ceive secondary-radiation from saidtarget', syn,-

chroniz-ing meansresponsive to saiddistribution circuit to synchronizet-he operation of each of, said-deflectingmeans-with the introduction of said. pulsed samples in eachof said cathode-ray tube circuits, and a commonoutput circuit--re'- sponsivetoreceivethe respective output currents from, each. of. said cathode-ray tubes whereby the. individual. currentsare added' togetherin overlapping. order, to produce ahmodified outputurrent.

6. A sysfcmicr translating anxapplied -signal;

said system comprisingin combinationan elec.

all of the same shape eachbaving anamplitudm 13 determined by the amplitude of the corresponding sample and a duration which exceeds the period of said sampling rate.

7. The method of signal translation which comprises continually deriving from an input signal regularly spaced samples varying in amplitude from one to another in conformity with and simulation of the variations in the amplitude of said signal, separately generating a corresponding succession of regularly spaced pulses all of the same predetermined shape, varying the magnitude of the successive pulses under the control of and in accordance with the magnitude of corresponding successive signal samples, combining the said pulses of varying magnitude and uniform shape to form an output signal, and removing from said output signal any frequency components lying above the frequency range occupied by said input signal.

8. The method of signal translation which comprises sampling an input signal at regularly WILLIAM R. BENNETT.

References Cited in the file of this patent UNITED STATES PATENTS Number Name Date 2,257,795 Gray Oct. 7, 1941 2,335,265 Dodington Nov. 30, 1943 2,464,607 Pierce Mar. 15, 1949 2,513,291 De Loraine et a1. July 4, 1950 

